Flood Hazard Assessment for a Hyper-Tidal Estuary as a Function … · 2018. 7. 20. · complex. Spatial and temporal variations in tidal levels, wave setup and rainfall and interaction

Flood Hazard Assessment for a Hyper-Tidal Estuary as a Functionof Tide-Surge-Morphology Interaction

Charlotte Lyddon1,2& Jennifer M. Brown2

& Nicoletta Leonardi1 & Andrew J. Plater1

Received: 19 July 2017 /Revised: 31 January 2018 /Accepted: 12 February 2018 /Published online: 7 March 2018

AbstractAstronomical high tides and meteorological storm surges present a combined flood hazard to communities and infrastructure.There is a need to incorporate the impact of tide-surge interaction and the spatial and temporal variability of the combined floodhazard in flood risk assessments, especially in hyper-tidal estuaries where the consequences of tide and storm surge concurrencecan be catastrophic. Delft3D-FLOWis used to assess up-estuary variability in extremewater levels for a range of historical eventsof different severity within the Severn Estuary, southwest England as an example. The influence of the following on flood hazardis investigated: (i) event severity, (ii) timing of the peak of a storm surge relative to tidal high water and (iii) the temporaldistribution of the storm surge component (here in termed the surge skewness). Results show when modelling a local area eventseverity is most important control on flood hazard. Tide-surge concurrence increases flood hazard throughout the estuary.Positive surge skewness can result in a greater variability of extreme water levels and residual surge component, the effects ofwhich are magnified up-estuary by estuarine geometry to exacerbate flood hazard. The concepts and methodology shown herecan be applied to other estuaries worldwide.

Keywords Flood hazard . Hyper-tidal . Severn estuary . Storm surge . Extremewater level . Delft3D

Introduction

Coastal zones worldwide are subject to the impacts of short-term, local variations in sea-level, particularly communitiesand industries developed on estuaries (Pye and Blott 2014).Extreme sea levels, caused by the combination of astronomicalhigh tides and meteorological storm surges, are a major threatto coastal communities and infrastructure (Elliott et al. 2014;Quinn et al. 2014;Webster et al. 2014; Prime et al. 2015). Thisis of particular significance in hyper-tidal estuaries, where tidalrange exceeds 6 m (Davies 1964; Robins et al. 2016).

Tidal range can exceed 6 m as tides are amplified throughan estuary due to near resonance, shallow bathymetry and

channel convergence (Archer 2013; Pye and Blott 2014).Surges can also be amplified through hyper-tidal estuaries,due to reduced hydraulic drag caused by greater mean depths,as seen along the Orissa coast of India (Sinha et al. 2008) andnarrowing topography and orientation of the coastline, as seenin the Cape Fear River Estuary, North Carolina (Familkhaliliand Talke 2016). Maximum water levels and storm surge im-pacts are not simply linearly related to increased tidal range(Spencer et al. 2015), but the complex interactions seen inhyper-tidal estuaries between tide, surge and landscape chang-es increases sensitivity to timing of storm events (Desplanqueand Mossman 2004), and thus exaggerate water levels. Tidalamplification and extreme surge development in hyper-tidalestuaries means concurrence of a large astronomical tide andextreme surge can be catastrophic, as seen in the Bay ofFundy, Canada (Desplanque and Mossman 1999), MeghnaEstuary, Bangladesh (As-Salek and Yasuda 2001) andSevern Estuary, UK (Pye and Blott 2010).

Accurate prediction of extreme water level and its timing isessential for storm hazard mitigation in heavily populated andindustrialised, hyper-tidal estuaries (Williams and Horsburgh2013). Such prediction requires accurate understanding of thetide-surge propagation, how this varies as a function of thetiming and shape of the storm surge relative to high water

Communicated by Arnoldo Valle-Levinson

* Charlotte [email protected]

1 School of Environmental Sciences, University of Liverpool, L697ZT, Liverpool, UK

2 National Oceanography Centre Liverpool, Joseph ProudmanBuilding, 6 Brownlow Street, Merseyside L3 5DA, Liverpool, UK

Estuaries and Coasts (2018) 41:1565–1586https://doi.org/10.1007/s12237-018-0384-9

# The Author(s) 2018. This article is an open access publication

http://crossmark.crossref.org/dialog/?doi=10.1007/s12237-018-0384-9&domain=pdf

mailto:[email protected]

and how such interaction changes due to estuary morphologyand bathymetry.

The Bay of Fundy, between the Canadian provinces ofNew Brunswick and Nova Scotia, has a maximum meanspring tidal range of 16.9 m which is the largest in the world(Greenberg et al. 2012). The tidal range is so large due to nearresonance with incoming North Atlantic tides (Desplanqueand Mossman 1999) and shallow water depths amplify thetide through the bay (Marvin and Wilson 2016). Shallow wa-ter depths and dimensions of the bay also amplify extra-tropical storm surges through the bay (Desplanque andMossman 2004). Therefore, when a surge coincides with anamplified, high astronomical tide, the results may be littleshort of catastrophic (Desplanque and Mossman 1999). Theconcurrence of a rapid drop in pressure and a ‘higher thannormal’ tide meant that water levels were elevated 2.5 mabove predicted level on the Groundhog Day storm, 1976(Desplanque and Mossman 2004).

The narrow geometry of the Qiantang River, east China,has a maximum tidal range of 7.72 m at Ganpu at its head andproduces one of the world’s largest tidal bores which reachesup to 9 m and travels up to 40 km/h (Pan et al. 2007; Zhanget al. 2012). On the Qiantang River, concurrence of high tideand typhoon-induced storm surges can raise observed waterlevels up to 10 m above predicted levels (Chen et al. 2014).

Extreme water level events are exaggerated in hyper-tidalestuaries due to the amplified tide-surge propagation, whichin turn can increase flood hazard. Flood hazard is defined asthe possibility of flood event occurring which could be dam-aging and harmful to communities and infrastructure (Shanze2006; Kron 2009). Expansion of the energy and agriculturalsector, migration and residential development in the coastalzone can increase flood hazard in estuaries (Pottier et al.2005; McGranahan et al. 2007). Shanghai, on the YangtzeRiver Estuary, is a centre for human population and economicactivities, with flood hazard further exacerbated by land sub-sidence (Wang et al. 2012a). Coastal flood hazard analysisaims to understand the processes and dynamics of coastalflooding to assess the potential consequences for people,businesses, the natural and built environment (Narayanet al. 2012; Monbaliu et al. 2014). However, the coastal floodsystem is a dynamic and complex system, with both physicaland human elements possibly exacerbating hazard. Decision-makers must therefore employ a variety of system level anal-ysis models and frameworks that account for key elements ofthe flooding system to understand the hazard (HRWallingford 2003).

The commonly used source-pathway-receptor-consequence(SPRC)model identifies key links between the built and naturalenvironment and sources of physical change (Gouldby andSamuels 2005; Horrillo-Caraballo et al. 2013; Oesterwindet al. 2016). This model was adopted by the EnvironmentAgency for local scale, coastal flooding to describe floodwater

propagation from source to floodplains, including physical pro-cesses and drivers, infrastructure and strategy (HRWallingford2004; Narayan et al. 2012). The first component of the SPRCmodel are the physical characteristics of flood hazard; sourceswhich may result in flooding events such as intense rainfall andstorm astronomical high tides and storm surges. However,quantifying sources in dynamic, interlinked systems can becomplex. Spatial and temporal variations in tidal levels, wavesetup and rainfall and interaction between sources, natural var-iability and combinations of sources are hard to account for(Sayers et al. 2002; HRWallingford 2003). Therefore, there isa need to better understand variability and combinations ofphysical processes driving local flood systems to improve floodhazard assessment.

Accurate prediction of the combination of factors driv-ing extreme water levels is a key component of understand-ing and assessing flood hazard (Pender and Néelz 2007).Numerical models can be used to simulate physical pro-cesses and calculate rates of change across time and spacethat result from different combinations of variables, e.g.meteorological conditions, tidal conditions and coastal de-fence systems (Lewis et al. 2013; Quinn et al. 2014).Analysis of extreme water levels requires a hydrodynamicmodel, which is able to simulate the flow and velocity ofwater, for example FVCOM, POLCOMS, TELEMAC andDelft3D (Jones et al. 2007). Two-dimensional, depth-averaged hydrodynamic models have previously been usedto successfully simulate the barotropic hydrodynamics inestuaries to help better understand past events, inform de-cisions concerning flood hazard and the development ofenergy resources and coastal defence intervention (Xiaet al. 2010; Wang et al. 2012b; Cornett et al. 2013;Maskell et al. 2014). These models rely on accurate ba-thymetry and boundary conditions when modelling coastaland estuarine areas to limit uncertainties in modelled re-sults (Pye and Blott 2014). Modelling studies which focuson the physical drivers of coastal flood hazard can aiddecision-makers and clarify connections in the system.

This research focuses on the Severn Estuary as an exemplarof hyper-tidal estuaries worldwide, due to its national signifi-cance for nuclear energy infrastructure (Ballinger andStojanovic 2010), and where complex interactions influenceextreme water level and subsequent flood hazard. TheBristol Channel and Severn Estuary, south-west England,is an example of a hyper-tidal estuary prone to relativelyfrequent meteorologically-induced surges generated byNorth Atlantic low-pressure systems (Uncles 2010). Forthe purposes of this paper, the ‘Severn Estuary’ is takento include the Bristol Channel. These storm surges can beexacerbated by the estuary’s dimensions and characteris-tics. The tidal range increases from 6.2 m in the outerBristol Channel to 12.20 m at Avonmouth as a functionof geometry (Pye and Blott 2014).

1566 Estuaries and Coasts (2018) 41:1565–1586

This paper uses the Severn Estuary, south-west England,as an example to describe the assessment of combinedflood hazard in the Severn Estuary resulting from astro-nomical high tides and meteorological storm surges. Asensitivity study is conducted using long-term tide gaugedata to force the model boundary of Delft3D-FLOW toinvestigate variability of extreme water levels. The effectof river flow on extreme water levels is not consideredhere, because the sensitivity of the Severn Estuary to riverflow is not as great as tidal and meteorological drivers.Also the greatest implications of flood hazard upon variousnuclear infrastructure will result from tide-surge propaga-tion especially because this is a hyper-tidal estuary. Riverflow would be an important factor to consider in estuarieswith smaller tidal ranges or greater discharge, e.g. PearlRiver Delta in China (e.g. Hoitink and Jay 2016;Leonardi et al. 2015). The results show the severity ofthe combined tide and storm surge event, timing of thepeak of the surge relative to tidal high water and the surgeskewness are important controls on flood hazard in estua-rine environments. This methodology can be applied toother estuaries worldwide, in the context of the SPRCmodel to help to better understand past extreme eventsand inform local management needs to minimise futureflood hazard.

Methods

Delft3D

Delft3D-FLOW, an open source, hydrodynamic model whichsolves depth-averaged unsteady shallow-water equationsacross a boundary fitted grid (Lesser et al. 2004), is used tosimulate barotropic tide-surge-river propagation and interac-tion in the Severn Estuary. The Delft3D-FLOW module hasbeen used in a number of studies to simulate tide-surge prop-agation and extreme water levels in a coastal environment(Irish and Cañizares 2009; Condon and Veeramony 2012).

Model Domain

The Severn Estuary model domain (Fig. 1) extends fromWoolacombe, Devon and the Rhossili, Gower Peninsula inthe West, up to Gloucester in the East, which is the tidal limitof the Bristol Channel (Pye and Blott 2010). The 2DH curvi-linear grid closely follows the coastline of the Severn Estuary.The horizontal model grid cell size varies from 3 km at theseaward boundary in the lower estuary to less than 10 m in theupper estuary. The model domain has two open boundaries: asea boundary forced by 15 min tide gauge water level data tothe West, and a river boundary forced by 15 min river gaugewater level data from Sandhurst to the East.

Gridded bathymetry data at 50 m resolution (SeaZoneSolutions Ltd. 2013) were interpolated onto the model grid.Lack of bathymetric data and poor resolution of data in theupper estuary meant that a uniform value had to be appliednorth of Epney to the river boundary. The value imposed was2 m, which represented a more realistic channel depth.Sensitivity analysis has been limited to external barotropictide-surge forcing and river discharge only and no meteoro-logical or wave forcings have been included in the model.Freshwater has not been considered as it has a lower impacton estuarine circulation and water levels. This is shown by theRichardson number, calculated by Reynolds andWest (1988),0.04–0.4 on spring tides, dependent on depth and breadth ofthe Severn Estuary. This is so impact of tide-surge propagationand external surge timing on extreme water levels up-estuarycan be assessed, which is likely to have the greatest impactupon various nuclear energy infrastructure assets within theestuary.

A 0.1 min time step is used to allow for calculations of theshallowwater equations to be solved in the fine resolution gridup-estuary. This is validated against the Courant number forthe grid. A uniform 0.025 Manning bottom roughness value isapplied to the grid.

Tide gauge locations in Fig. 1 indicate where long-termwater level records are available, with which to compare andvalidate the model results.

Boundary Conditions

Long-Term Tide Gauge Data

Long-term tide gauge records from The Mumbles (Fig. 2a)and Ilfracombe (Fig. 2b), located close to the western bound-ary of the model domain, are used to force the total and tidalwater levels in different model setups. The long-term tidegauge records, collected by the UK Tidal Network (https://www.bodc.ac.uk/data/online_delivery/ntslf/), provide hourlysampled tidal records prior to 1992 and quarter hourlysampled tidal records from 1993 to present day. All highwater peaks (astronomical tide + storm surge) in the recordfrom Ilfracombe and The Mumbles were identified andisolated. Sea-level values flagged in the tidal record by theBritish Oceanographic Data Centre (BODC) as improbable,null or interpolated values were discarded, to ensure only ac-curate observational data are used to force the modelboundary.

While joint probability distribution analysis is a commonapproach to defining event severity (McMillan et al. 2011a;Williams et al. 2016), here we use percentile values applied tolong-term monitoring data. This is because many tide-surgewater level combinations have the same severity, making ithard to choose a single event. Although return period analysisprovides a statistically representative event, we use observed

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events and classify their severity against long-term records bythe use of percentile values. To identify extreme events atIlfracombe and The Mumbles, we calculated the 99th, 95thand 90th percentile values of the high water levels and createda set of severity thresholds. Extreme water level events ex-ceeding the 90th, 95th and 99th percentile severity thresholdsare identified. Four extreme water level events for which apositive surge occurs and a complete total water level seriesare available at Ilfracombe or TheMumbles and the tide gaugelocations up-estuary (Hinkley, Newport, Portbury, Oldbury,Sharpness, Fig. 1) for validation purposes are identified.Using the Environment Agency return period for still water,extreme sea level values these events fall within the rangebetween a 1/1 (5.41 m) and 1/100 (6.03 m) year event(McMillan et al. 2011b). A historical water level event whichfalls within the 1/200 year category would be defined as amore severe event. Missing data in the tide gauge recordsdid not allow for data from both Ilfracombe and TheMumbles to be interpolated across the seaward open boundaryin the model.

Small differences are present in the tide-gauge recordsfor amplitude and phase between Ilfracombe and TheMumbles. The maximum difference in phase between highwater points is 15 min, with high water occurring later atThe Mumbles. Small differences occur in amplitude, witha higher water level occurring at the Mumbles, to theorder of tens of centimetres. It is likely that tide and surgeeffects that occur over a region could be coherent atneighbouring stations (Proctor and Flather 1989). The dif-ferences could also be an artefact of the recording fre-quency and could potentially be smaller than observed.Therefore, differences in phase and amplitude are

considered small enough to impose conditions from eitherlocation across the sea boundary in a uniform manner.

River level data from Sandhurst river gauge station, locatedjust north of Gloucester, is used to force the eastern modelboundary. The river level data is converted to chart datum,to match the model datum.

Surge Characteristics

The extreme water level event is isolated as a storm tide, 6 hbefore and 6 h after the maximum water level. Water leveltime series are isolated from the tide gauge record from 3 daysprior to and 2 days after the storm tide peak; each model runscenario is 5 days long. Following these criteria, it can be seenthat only events since 2012 are taken from the tide gaugerecord. A notably stormy winter in 2013/2014 coincided withthe peak of the 18.6 year tidal lunar cycle (Gratiot et al. 2008;Haigh et al. 2016).

The surge component time series during the 5-day sim-ulations is separated from the total water level time series.Long-term tide gauge records provide information on bothtotal water level and residual surge. The residual surge iscalculated as the total observed water level minus the pre-dicted tide, taken from POLTIPS3 which is available fromthe National Tide and Sea Level Facility (Prime et al.2015). This way, any tide-surge interaction remains withinthis residual surge component. A Chebyshev type II, lowpass filter is applied to the residual surge component toseparate out the time-varying meteorological residual andthe tide-surge interactions (an approach used by Brownet al. 2014). The low pass filter is designed to remove allenergy at tidal frequencies, using a stop-band of 26 h and a

Fig. 1 Severn Estuary model domain. The bathymetry is relative to chart datum (CD)


pass-band of 30 h. A 3 dB pass-band ripple and 30 dBstop-band attenuation was used, to leave only the meteoro-logical residual (low-frequency surge component with notidal energy or tide-surge interaction) in the time series.Tidal energy and tidal interaction is removed, as it has asimilar frequency to the tide and leaves only the low-frequency (> 30 h, sub-tidal) residual (Brown et al. 2014).The low pass filter approach was validated using the 25 hrunning mean of the surge component.

Storm surge features are characterised by the skewness ofthe residual surge component with time. Skewness is a mea-sure of the asymmetry of the data around the time series

mean (Growneveld and Meeden 1984). The skewness of adistribution is defined as follows:

skewness ¼ NN−1ð Þ N−2ð Þ Σ

xi−�xs

� �3

where N is the number of observations, xi is the ith observa-tion, �x is the mean of the observations and s is the standarddeviation of the sample (Groeneveld and Meeden 1984).Positive skewness describes a shorter, steeper rising limb onthe surge; negative skewness refers to a shorter, steeper fallinglimb following the maximum surge.

Fig. 2 a Long-term tide gauge record at The Mumbles, Bristol Channel,UK showing tide gauge time series, points in the time series representinghigh water peaks and events to be modelled. The panels on the rightillustrate the three selected events representing the 95th (i, 14thDecember 2012), 90th (ii, 18 December 2013) and 99th (iii, 3 January

2014) water level percentile values. b Long-term tide gauge record atIlfracombe, Bristol Channel, UK showing tide gauge time series, pointsin the time series representing high water peaks and events to bemodelled. The panel on the right illustrates one selected eventrepresenting the 95th (i.e. 5 May 2015) water level percentile values


Two events have a surge component with positive skew-ness, and two with negative skewness. The skewness value ofthe filtered surge component as defined in this manuscript(asymmetry of the shape of the surge curve) must not be con-fused with a ‘skew surge’ (the difference between the maxi-mum observed water level and the maximum predicted tidallevel, regardless of timing (de Vries et al. 1995)).

To investigate the effects of skewness of the surges onextreme water level, four historical events are presented basedon the characteristics of the filtered residual surge componentwith time (Fig. 3).

Results from the 99th water level percentile event (3January 2014), the most extreme event on record, shows ahigh, positive skewness value of 0.59 from the filtered surgedata. This indicates that the surge has a longer falling limb; theinfluence of the surge is extended over time after the peak ofthe surge. The filtered surge component for the 90th waterlevel percentile event (18 December 2013) shows a lower,positive skewness value of 0.41. This is a lower skewnessvalue than the 99th water level percentile event (3 January2014), but still indicates a longer falling limb of the surgecurve.

The filtered surge component for the 95th water level per-centile event (5 May 2015) shows a negative skew value of −0.45. This indicates a long rising limb of the surge. The fil-tered surge component for the 95th water level percentileevent (14 December 2012) shows a negative skewness valueof − 0.14. This value also still indicates that the filtered surgecomponent has a longer rising limb; the influence of the surgeis extended over time before the peak of the surge.

Timing of Surge Occurrence

The filtered surge component is recombined with the predict-ed tide at the tide gauge locations in a range of different time-shifted configurations (McMillan et al. 2011a). The peak of

the surge changes in time relative to the peak of high water toinvestigate the influence of the timing of the surge on the totalwater level throughout the estuary.

The first time series represents the realistic timing of thepeak of the surge relative to high water for each extreme waterlevel. An additional 13 time series are created with the peak ofthe surge changing relative to the peak of high water. Startingfrom a configuration where the peak of the surge coincideswith the peak of high water, the peak is then advanced incre-mentally to 6 h before and delayed equally incrementally to6 h after high water to cover 1 full tidal cycle.

A total of 16 model runs are thus completed for each his-torical extreme water level event (Table 1). One validation runis completed for each historical event to ensure the model canreproduce the tide gauge data at stations up-estuary. For thisvalidation model run, the boundary is forced by the total waterlevel time series from Ilfracombe or The Mumbles tide gauge.A ‘tide only’model run is simulated to provide a baseline, anda number of filtered surge plus tide model runs are simulatedto represent the possible timings of the peak of the surgerelative to predicted tidal high water.

Model Validation

Water level time series at tide gauge locations in the estuaryare isolated from the model outputs. The model is initiallyvalidated using the most extreme event on record; with astorm tide peak which occurred at 07:15 on 3 January 2014.The model has been validated at the coast to observation datafrom tide gauges up-estuary, using data from the UK TidalNetwork, Environment Agency and Magnox at Oldbury.Error metrics (R2, RMSE, Willmott Index of Agreement(Willmott 1981; Willmott et al. 2012), Bias of the maximumvalue)) are calculated at tide gauge locations up-estuary formodel runs with realistic timings of the surge peak relative totidal high water (total water level, filtered surge + tide) and the

Fig. 3 Normalised filtered surgeshape component with time,characterised by historical eventseverity and skewness (measureof asymmetry)


tide only simulation to provide a baseline. Error metrics con-firm if the model can reproduce observational tide gauge dataand assess the error introduced by this methodology.

Figure 4a illustrates validation runs and observational datafor Hinkley Point; there is good graphical and statistical agree-ment between the model output (dashed lines) and observa-tional data (solid line). The model is able to reproduce the tidegauge data at Hinkley Point well, with an R2 value of 0.996(Table 2). High water levels are over estimated, as confirmedwith a bias value of 0.242, by 15–20 cm. However, this rep-resents just 1.5% of the overall tidal range (12.29m at HinkleyPoint).

The ‘tide only’ model provides a baseline which subse-quent model runs can be compared with, as there is no mete-orological influence. It can be seen the ‘tide only’model run isnot resolving the high water peaks as there is no meteorolog-ical influence, and the low water is underestimated, as shownby the negative bias value. There is a bias away from the tidegauge data in a negative direction—the values are all lowerthan the observation data. The tidal phase is successfullyreproduced. The tide + filtered surge model run, where thereis no change in timing of the surge from the real event, alsooverestimates low water. The tide + filtered surge model run isvery similar to total water level simulation, suggesting thatexternal tide-surge interaction, which has been filtered out ofthe boundary conditions, has a small contribution.

Figure 4b shows how the model has been tested furtherup-estuary, at Sharpness, using river gauge data from theEnvironment Agency. The quality of bathymetry and ge-ometry of the long, shallow, narrow channel of the RiverSevern strongly influence the model results up-estuary.The lower Index of Agreement and R2 value and higherRMSE and bias (Table 3) for the ‘tide only’ model runindicates that surge has a large contribution to total waterlevel in this location up-estuary. There remains goodgraphical and statistical agreement between model runs(dashed line) and tide gauge data (solid line). Figure 4b

shows that the model is able to capture tidal asymmetry,which refers to the interaction between tidal wave propa-gation and shallow water impacts due to changes in widthand depth of the channel up-estuary (Uncles 1981; Pye andBlott 2010).

The tidal phase is in good agreement; however, some of thehigh water points are not achieved, which is likely to be due toerror in the low-resolution bathymetry influencing the propa-gation of the tide in the upper estuary; the bathymetric surveywill not match the bathymetry at the time of the event. Errorsin bathymetry and flushing can explain the poorer simulationof low water than high water at both locations.

The model is in good agreement without the inclusion ofmeteorological forcing and waves, confirming that the ap-proach is adequate to capture spatial variations in extremewater levels.

Funnelling Effect vs Frictional Effect

The greatest maximum water elevation along the thalweg ofthe estuary is 8.12 m at 108 km up-estuary, beyond Portbury,when the peak of the surge occurs 15 min before the peak ofhigh water on 3 January 2014 (99th percentile). It can be seenin Figs. 5 and 6 that the maximum water elevation, along thethalweg of the estuary, during each of the four events consis-tently occurs close to Portbury. After this point, the maximumwater elevation begins to fall again.

The tidal amplitude along estuary is determined by com-peting processes of tidal damping due to friction, and tidalamplification due to funnelling effect and reflection. Fromthe mouth of the estuary up to Portbury, the funnelling effectdominates to amplify the tidal wave as it propagates up theestuary (Dyer 1995). Mean spring tidal range increases up-estuary towards Portbury due to the funnelling effect of coast-al topography, the continuously upward slope of the basin andnear-resonance of the estuary to the M2 tidal period (Uncles1981; Liang et al. 2014). Portbury has the second largest meanspring tidal range in the world, approaching 12.2 m (Uncles2010). Beyond Portbury, the funnelling effect is counteractedby friction. Friction acts to dampen the propagation of the tidalwave (Proudman 1955a). This balance between the funnellingeffect and friction determines where overall maximum waterlevel will occur in the estuary.

The sensitivity of the model domain to an applied frictionvalue and the point where the friction and funnelling effect isbalanced is investigated.

A higher friction value (Manning = 0.075) and lowerfriction value (Manning = 0.013) was applied to the modeldomain for the 99th water level percentile event (3 January2014) model runs. The range in maximum water elevationsalong the deepest channel of the estuary for results of thealtered friction values are compared to the original modelrun (Manning = 0.025).

Table 1 Scenarios modelled in Delft3D for each historical extremewater level event

Model run scenario Purpose

Total water level Validation

‘Tide only’ Baseline

Tide + surge Baseline

Tide + filtered surge at 0 min Sensitivity timing studyTide + filtered surge at ± 15 min

Tide + filtered surge at ± 30 min

Tide + filtered surge at ± 45 min

Tide + filtered surge at ± 1 h




Figure 5 shows that a higher friction value dampens theamplitude of the water elevation from the mouth up-estuary;the funnelling effect has little influence here and there is noobvious tipping point between funnelling and friction. A low-er friction value means the funnelling effect significantly am-plifies the tidal wave up-estuary, producing water elevationsbeyond those that would realistically be seen in this estuary.The tipping point between funnelling and friction moves upbeyond Oldbury.

The response of the model to changing friction followsthe characteristic of tidal response in estuaries (Dyer 1995).

Under a friction value of 0.025, the estuary shows ahypersynchronous response (Fig. 5i) where funnelling effectexceed frictional effects with increasing tidal range up to apoint where friction then dominates, due to the shallow,narrow channel morphology. With a low friction value,the estuary responds in a more extreme hypersynchronousmanner. Funnelling effects exceed frictional effectsthroughout the estuary and tidal range continues to in-crease further up-estuary. Under a high friction value, themodel responds in a hyposynchronous manner (Fig. 5 ii).Friction dominates and tidal range diminishes through the

Fig. 4 aValidation down-estuary,Hinkley Point tide gauge. bValidation up-estuary, Sharpnessriver gauge. As above

Table 2 Statistical validationdown-estuary, Hinkley tidegauge. The filtered surge isapplied at a realistic time relativeto tidal high water for validationpurposes

Total water level ‘Tide only’ Tide + filter surge

R2 0.996 0.909 0.955

RMS error 0.172 0.255 0.212

Willmott index of agreement 0.969 0.913 0.946

Bias of maximum value 0.242 − 0.91 − 0.556


estuary. The funnelling vs friction effect is likely to be adominating factor in the hydrodynamics of the SevernEstuary, with a change in friction value in the model do-main changing where maximum tidal range occurs. Underfuture sea levels and saltmarsh extents, the estuary dynam-ics under extreme could change the spatial variability inextreme water levels.

Results

Model outputs are analysed to identify how the total waterlevel, and consequently flood hazard, and local interactionschange up-estuary, for different timing of surge occurrence,and surge characteristics. Results are presented systematicallyfor the four extreme events previously selected.

In the first part of the results, variations in maximum waterlevel values along the estuary thalweg, and for different timingof surge occurrence are presented. Changes in water level as afunction of surge skewness, and percentile are presented.After that, we will use the following plots as flood hazardproxies at each tide gauge location up-estuary:

i) Percentage change in maximum total water level com-pared with the ‘tide only’ model run is plotted as afunction of change in timing of surge at the modelboundary

ii) Percentage change in the time integrated elevation, i.e.the area (m2/s) under the curve of the peak of the stormtide event, exceeding Mean High Water Spring(MHWS) compared with the model run when the peakof the surge and high water coincide (0 min)

iii) Percentage change in duration (minutes) of the peak ofthe storm tide event exceeding MHWS, calculated byinterpolating between time steps exceeding the MHWSelevation, compared with the ‘tide only’ model run

iv) Percentage change in maximum total surge elevation,compared with the 0 min model run when the peak ofthe filtered surge and tide coincide; the total surge iscalculated by removing the modelled tidal time seriesfrom all total water level model run scenarios, and in-cludes a tide-surge interaction component and a mete-orological component. The tide-surge interaction gen-erates harmonics at tidal frequencies, which means thatrelative contributions cannot be separated

Fig. 5 Water level along the deepest channel in the Severn Estuary, 3January 2014, under varying Manning friction values (99th percentile);the shading represents the range in results for each filtered surge time shift

scenario. Subpanels show the tidal response of i) hypersynchronous andii) hyposynchronous estuary to changing frictional effects

Table 3 Statistical validation up-estuary, Sharpness river gauge Yotal water level ‘Tide only’ Tide + filter surge

R2 0.985 0.897 0.937

RMS error 0.157 0.62 0.206

Wilmott index of agreement 0.9856 0.787 0.97

Bias of maximum value 0.634 − 0.609 − 0.746


MHWS is used as the baseline for proxy calculations as thisis the reference level for all sea defence designs (McMillanet al. 2011a). All calculated water levels, areas and timingsapply to the peak of the storm tide event within the 5-daysimulation. The storm tide event is defined as 6 h before and6 h after the maximum peak of high water in the time seriespeak. Correlation between each flood hazard proxy, skewnessof the filtered surge component and severity of the event isanalysed.

Water Level Variations Along Estuary

Figure 6a–d shows maximum water elevation every 2 kmalong the thalweg of the main channel of the Severn Estuary(Fig. 1) over the duration of the simulation, for each shift inthe timing of the peak of the surge relative to tidal high water.The plots illustrate how maximum water elevation changesup-estuary.

It is noticeable from Figs. 6a–d that there is sensitivity tothe timing of the peak of the surge relative to tidal high waterand there are noticeable changes inmaximumwater elevationsalong the deepest channel of the estuary for each time-shiftedconfiguration. Maximum range in water elevations due tosurge timing occurred for the 90th and 99th percentile events.

For the 90th water level percentile event (18 December2013), the highest water elevation down-estuary is seen whenthe peak of the surge occurs 6 h before the peak of high water.The maximum water elevation down-estuary is consistently0.2–0.25 m higher than the 0 min scenario when the peak ofthe surge occurs 6 h before the tidal peak. There is a change in

which scenario results in the highest water elevation at106.5 km up-estuary. In the upper estuary, the highest waterelevation is seen when the peak of the surge occurs 6 h afterthe peak of high water. The water elevation is consistently0.1–0.35 m higher than the 0 min scenario, when the peakof the surge occurs 6 h after the tidal peak.

For the 99th water level percentile event (3 January 2014),the highest water elevation down-estuary is seen when thepeak of the surge occurs 1 h after the peak of high water.The maximum water elevation down-estuary is consistently0.2–0.25 m higher than the 0 min scenario when the peak ofthe surge 1 h after the tidal peak. The minimum water eleva-tion down-estuary is 0.1–0.15m lower than the 0 min scenariowhen the peak of the surge occurs 6 h before high water. In theupper portion of the estuary, the highest water elevation con-sistently occurs 0.01–0.05 m higher than the 0 min scenariowhen the peak of the surge is 30, 45 or 60 min after highwater: there is no scenario which consistently results in themaximum water elevation. However, the lowest water eleva-tion in the upper portion of the estuary is consistently a resultof when the surge peak is 6 h before the tidal peak, and is up to0.25 m lower than the 0 min scenario.

It is noticeable in Fig. 6a–d that change in time of the peakof the surge relative to high water causes little variability in themaximum water elevation in the lower estuary, and greatestvariability in water elevation between time shift scenarios be-yond Portbury, 106 km up-estuary.

Figure 7 shows the range of maximum water elevationevery 2 km along the thalweg for all time shift configurations.The range of values are coloured according to the skewness of

Fig. 6 a Maximum water level in the Severn Estuary, 99th water levelpercentile event (3 January 2014). bMaximum water level in the SevernEstuary, 95th water level percentile event (14 December 2012). c

Maximum water level in the Severn Estuary, 90th water level percentileevent (18 December 2013). d Maximum water level in the SevernEstuary, 95th water level percentile event (5 May 2015)


the surge component with time, and also classified based onthe severity of the extreme event.

The greatest range between maximum and minimum waterelevation across the surge time shift scenarios is 0.44 m for the90th water level percentile event (18 December 2013) and0.27 m for the 99th water level percentile event (3 January2014). Deviations in water level are not uniform along theestuary, and the 90th water level percentile event shows apositive shift in water level in the lower part, and negativeshift in the upper part. The surge component of both theseevents has a positive skewness value. The smallest range be-tween maximum and minimum water elevation across thesurge time shift scenarios is 0.03 m, for 95th water level per-centile event (14 December 2012). This event has a surgecomponent with a negative skewness value.

The surge components which have a positive skewnessvalue, a steeper rising limb and a longer falling limb showthe greatest range of water elevation values along the deepestchannel of the estuary. The range of values increases up-estuary, with the greatest range in water level values occur-ring beyond Portbury. This indicates that location in theupper estuary may be more sensitive to changes in thetiming of the peak of a surge which displays a positiveskewness. The surge components which have a negativeskewness, a longer rising limb and steeper falling limbshow a more constrained range of maximum water eleva-tions and there is less sensitivity throughout the estuary tothe timing of the surge peak.

The maximum water elevations are stacked on top of eachother according to severity of the event. It can be seen that the99th water level percentile event (3 January 2014) consistentlyresults in the greatest maximum water elevations along the

thalweg of the estuary. The 95th percentile events show lessextreme maximum water elevations in the estuary. There isapproximately a 1 m difference between the 95th water levelpercentile event (14 December 2012) and 95th water levelpercentile event (5May 2015). The 95th water level percentileevent (5 May 2015) initially shows similar water level valuesto the 90th water level percentile event (18 December 2013),before increasing beyond this 90th percentile event. As ex-pected, the 90th water level percentile event (18 December2013) shows the lowest maximum water elevations alongthe deepest channel of the estuary.

It is also evident in Figs. 6 and 7 that the maximum waterelevation for all extremewater level events consistently occursclose to Portbury, the location for maximum observed tidalrange in the estuary (Pye and Blott 2014).

Changes in Flood Hazard Proxy with Surge Timing

Figures 8, 9, 10 and 11 show changes in flood hazard up-estuary in locations where nuclear assets and/or tide gaugesare located, as a function of change in timing of the surge atthe model boundary. Each flood hazard proxy (maximum totalwater level, maximum total surge, time integrated elevationand duration exceeding MHWS) is calculated from the stormtide peak: 6 h before and 6 h after high water. All data aredisplayed as percentage change, compared with the ‘tide only’model scenario, apart from maximum total surge which iscompared with the model run when the peak of the surgeand high tidal water coincide (‘0 min’).

Figure 8 shows flood hazard at each tide gauge location fora 99th water level percentile event (3 January 2014), the mostextreme event on record.

Fig. 7 Range of water level values for time shift configurations along deepest channel of the Severn Estuary when overall maximumwater level occurs.For each event, in the legend, the first value represents the percentile of the event and the second value is the skewness


The greatest percentage change in maximum total waterlevel between each time shift scenario and the ‘tide only’scenario is seen in tide gauge locations down-estuary, notablyHinkley Point and Newport (up to 10.02%). Tide gauge loca-tions down-estuary, Hinkley Point, Portbury and Oldburyshow symmetry in the results: the highest maximum waterlevel happens when the surge occurs at the same time as highwater. The magnitude of the maximum total water level thenreduces when the peak of the surge occurs before or after thepeak of high tide.

There is less percentage change in maximum total waterlevel at tide gauge locations further up-estuary. The greatestpercentage change in maximum total water level occurs whenthe peak of the surge happens 3 h after the peak of high water.This is particularly clear at Sharpness, up to 8%.

There is a noticeable linear trend in the percentage changeof maximum total surge value which occurs ± 6 h of the stormtide peak, compared with the 0 min scenario. The greatestpositive percentage change in maximum total surge elevationcan be seen when peak of the surge occurs after 6 h after thepeak of tidal high water. A similar magnitude of negativepercentage change in maximum total surge can be seen whenthe peak of the surge occurs 6 h before the peak of tidal highwater. There is little sensitivity of maximum total surge eleva-tion to the timing of the surgewhen the peak occurs around thetime of high water, and there is also little spatial variability

between the locations. There is increased variability in maxi-mum total surge elevation across the estuary with greater shiftaway tidal high water. The greatest variability can be seenwhen the peak of the surge occurs significantly after tidal highwater. Portbury shows the greatest positive percentage changein maximum total surge elevation (32.5%) when the peak ofthe surge occurs 6 h after tidal high water. This could be linkedto the positive skewness of the surge with greater influenceafter the peak.

The maximum change in duration of peak of the storm tideexceeding MHWS is seen at locations down-estuary, HinkleyPoint and Newport. Portbury and Oldbury show the greatestchange in duration when the peak of the surge occurs 1–3 hafter the peak of high water. There is a smaller percentagechange in duration of the storm tide peak exceeding MHWSfurther up-estuary, at Sharpness. These tide gauge locationsshow asymmetrical results, with the greatest change in dura-tion when the peak of the surge occurs 3 h before the peak ofhigh water.

The greatest change in time-integrated elevation of thepeak of the storm tide exceeding MHWS is seen at HinkleyPoint, with the greatest area exceeding MHWS when thepeak of the surge occurs at the same time relative to thepeak of high water. Model results from Portbury andNewport also show over 28% change in time-integratedelevation (m2) exceeding MHWS. Locations further up-

Fig. 8 3 January 2014. Floodhazard proxy calculated at eachtide gauge location. a Percentchange in maximum water level.b Percent change in maximumtotal surge elevation. c Percentchange in duration exceedingMHWS. d Percent change in areaexceeding MHWS. All data isdisplayed as percentage change,compared with the tide onlymodel scenario, apart from non-linear interaction which iscompared with the model runwhen the peak of the surge andhigh water coincide


estuary, Oldbury and Sharpness, consistently show lowerpercentage change within the range of 17–21%. These re-sults are also symmetrical, with the greatest percentage ofchange in area when the peak of the surge occurs at thesame time as the peak of high water.

Figure 9 shows flood hazard at each tide gauge location fora 95th water level percentile event (14 December 2012). Thegreatest percentage change in maximum total water level be-tween each time shift scenario and the ‘tide only’model run isseen in tide gauge locations down-estuary, at Hinkley Pointand Newport, up to 5%. Oldbury is located further up-estuary,where the channel of the River Severn begins to narrow, butstill shows a greater percentage change than Portbury. Thechange in maximum water level for this event is not to thesame extent as the 99th water level percentile event (3 January2014). Sharpness shows the smallest percentage change inmaximum total water level, compared with the ‘tide only’model run. All results show a symmetrical shape, with thegreatest change in total maximum water level when the peakof the surge coincides with the peak of high water. Thesmallest percentage change in maximum water level occursat all locations up-estuary when the peak of the surge occurs6 h after the peak of high water.

The linear trend in percentage change of maximum totalsurge elevation for a 95th water level percentile event (14December 2012) is similar to 99th water level percentile event

(3 January 2014), with the changing time of the peak of thesurge relative to tidal high water. The greatest positive per-centage change occurs when the peak of the surge occurssignificantly after tidal high water, at Hinkley Point (21.2%)and Portbury (17.8%). The greatest variability and magnitudein percentage change of maximum total surge elevation occurswhen the surge occurs 6 h before the peak of tidal high water.This could be linked to the negative surge skewness, withgreater influence before the peak of the surge. There is lessvariability in maximum total surge elevation when the surgeoccurs 6 h after tidal water.

The greatest percentage change in duration of the peak ofhigh water exceeding MHWS is in locations down-estuary,notably Hinkley Point and Newport, up to 29.2%. These lo-cations also show a symmetrical trend; the greatest percentagechange is when the peak of the surge occurs at the same timeas the peak of high water. The locations are stacked on top ofeach other, which is determined by the location up-estuary.There is a notable gap in percentage change in duration be-tween locations in the lower estuary (Hinkley Point, Newport)and the upper estuary (Sharpness, Oldbury). Greatest durationat Oldbury and Sharpness is when surge occurs 1 h beforehigh water.

The greatest percentage change in area of the peak of highwater exceedingMHWS is in locations down-estuary, notablyHinkley and Newport, up to 30.5%. Locations are stacked on

Fig. 9 14 December 2012. Floodhazard proxy, as in Fig. 8


top of each other, as a function of the distance up-estuary. Alllocations show symmetrical trends as the peak of the surgechanges relative to high water; the greatest change in area iswhen the peak of the surge and tide coincide. In addition tothis, there is less variation between each time shift, and resultsat each location appear flatter than changes seen in maximumtotal water level and duration of peak exceeding MHWS.

Figure 10 shows flood hazard at each tide gauge locationfor a 95th water level percentile event (5 May 2015). Thegreatest percentage change in maximum total water level,compared with the ‘tide only’ model run, is seen at HinkleyPoint, Newport and Portbury, up to 8.6%. As seen in otherfigures, the locations are stacked on top of each other based ontheir distance up-estuary. Epney, for example, shows smallestpercentage change. All locations show least percentagechange at − 6 h.

The linear trend in percentage change of maximum totalsurge elevation is also noticeable for 5 May 2015. There is asmaller overall magnitude of positive and negative percentagechange compared to the other events. Sharpness showsgreatest negative percentage change (− 10%) and Oldburyshows greatest positive percentage change in maximum totalsurge elevation (8.6%). Newport shows little sensitivity to thechanging time of the peak of the surge relative to high water.There is less variability between locations, excludingNewport, when the peak of the surge occurs significantly be-fore or after tidal high water.

The storm tide peak exceeds MHWS at all locations for a95th water level percentile event (5 May 2015). Hinkley Pointshows the greatest percentage change in duration of the stormtide peak exceeding MHWS, but there are small changes be-tween each time shift scenario.

The greatest change in duration at Portbury occurs at– 15 min (11.725%), followed by 0 min (11.72%) and– 30 min (11.71%). Small percentage changes occur acrossall locations (within 0.1% change in duration) when the surgeoccurs within 1 h of high water. The lowest percentage changeat all locations occurs when the peak of the surge occurs 6 hafter the peak of high water. This could be due to the influenceof the characteristics of the filtered surge that has beenmodelled for this historical event.

Figure 11a shows flood hazard at each tide gauge locationfor 90th water level percentile event (18 December 2013).Down-estuary locations, at Hinkley Point, Newport,Portbury and Oldbury, show a similar percentage change inmaximum total water level, up to 7%, compared with the ‘tideonly’ model run. The smallest percentage change is seen atSharpness. All locations show a jump inmaximumwater levelat + 6 and – 6 h, which could be due to the influence of theshape of the surge, as the other time shifts show a flatter trend.

The linear trend in percentage change of maximum totalsurge elevation in Fig. 11a (ii) is similar to other events. Thereis greater variability between locations when the peak of thesurge occurs 3 or 6 h before and after tidal high water like the

Fig. 10 5 May 2015. Floodhazard proxy, as in Fig. 8


99th water level percentile event (3 January 2014). This couldbe linked to surge skewness like the 3 January 2014. Thegreatest magnitude of percentage change can be seen whenthe peak of the surge occurs significantly before tidal highwater. The greatest positive (29.08%) and negative (−47.57%) percentage change in maximum total surge elevationoccurs at Sharpness. Newport shows less sensitivity to thetiming of the peak of the surge relative to high water, with arange of 20.1% and a more symmetrical trend.

The peak of the storm tide only exceeds MHWS atSharpness and Oldbury when the 18 December 2013 eventis simulated, likely to be because it is a 90th percentile event.Oldbury shows a clear percentage change because the ‘tideonly’ scenario (6.821 m), which all time shift scenarios arecompared with, does not exceed MHWS (7.02 m). The surgeis having a noticeable influence on the time the peak of thestorm tide exceedsMHWS at these locations. Figure 12 showsthat Sharpness has an asymmetrical trend with the greatestpercentage change in duration (19.9%) when the surge occurs45 min after high tide.

Oldbury also shows a noticeable percentage change forarea exceeding MHWS compared with the ‘tide only’ modelrun, and a very small value for Sharpness (Fig. 12). Sharpnessshows a small range of 0.1% between time-shift scenarios.The greatest change in area (3.9%) happens when the surgeoccurs 1 h after high tide.

Discussion

Physical Drivers and Sources of Flood Hazardin the Severn Estuary Model Domain

Delft3D-FLOW is used to simulate barotropic tide-surgepropagation, river flow and interaction in the Severn Estuaryacross a 2DH grid. Results from four historical events arepresented which show the influence of the severity of thestorm surge, the influence of the timing of the surge on thetotal water level and characteristics of the filtered surge com-ponent on the total water level throughout the Severn estuary.The results presented here can help to identify variability inthe sources of an extreme water level event in a hyper-tidalestuary, which can contribute towards flood hazard. Theseresults can help to inform local management needs in ahyper-tidal estuary when viewed in the context of thesource-pathway-receptor-consequence (SPRC) conceptualmodel (Shanze 2006).

Influence of Storm Severity on Extreme Water Levels

The results suggest that severity of the event is an importantcontrol on the magnitude of extreme water levels throughoutthe Severn Estuary. The 99th water level percentile event (3January 2014) consistently produced greatest water elevations

Fig. 11 18 December 2013.Flood hazard proxy as in Fig. 8


along the deepest channel of the estuary and greatest percent-age change in maximum water levels at all sites. A moresevere storm surge event, driven by low atmospheric pressure,wind speed, wind direction and storm duration (Woth et al.2006), increases extreme water levels throughout in theSevern Estuary and is an important driver of flood hazard.Extreme tidal levels are known to be the predominant driverof flooding events in the Severn Estuary, particularly in loca-tions close to the maximum MHWS at Avonmouth (CapitaSymonds 2011). A 3.54 m (11.6 ft) surge was recorded atAvonmouth in March 1947 (Heaps 1983), attributed to verylow pressure (974 mb, which is 38 mb below normal regionallevel) and predominantly easterly track of the depression(Lennon 1963), indicating the severity of a storm surge eventis a combination of meteorological factors.

The 99th percentile water level events may be a rare occur-rence, and equal consideration should be given to the effect ofmore frequent, less severe events in the estuary. However,much of the UK is defended against high-frequency, low-magnitude events up to a 1:200 year event, therefore reducingflood hazard. An understanding that a more severe, extremewater level event can increase flood hazard can be used bylocal coastal planners to manage flood risk and can aid oper-ational flood management (Menéndez and Woodworth 2010).If the severity of an event can be forecast then warnings can beissued to appropriate authorities and the public (FLOODsite2005). Event severity is an important control when modellingto extreme water levels on a local scale.

Influence of the Timing of the Peak of the Surge

The timing of the peak of the storm surge relative to tidalhigh water is another important contribution to the physicaldrivers of flood hazard at the coast. There is sensitivity tothe timing of the peak of the surge throughout the Severn

Estuary model domain. This is particularly evident in theupper estuary; when the peak of the surge occurs 2–6 hafter high water, there is a greater percentage change inmaximum water level. Increased water depth at the timeof tidal high water could induce surge propagation throughthe estuary (Wolf 2009) to increase extreme water levelsup-estuary. Increased water depths would limit shallowwater and quadratic friction effects on the tidal amplitude.However, at these shifts, the flood hazard (area and dura-tion of the storm tide peak exceeding MHWS) is lower.

There is less sensitivity to changes in the timing of thesurge in the lower estuary, notably Hinkley Point. The greatestpercentage change in maximum water level occurs when thepeak of the storm surge and tide coincide. The concurrence ofhigh tide and storm surge peak in the Severn Estuary hasresulted in extreme water levels in the past (Lennon 1963).The highest recorded water level in the Severn Estuary in acentury occurred during the storm 13December 1981 (Proctorand Flather 1989). A fast moving secondary depression, track-ing further south than usual for the time of year, producedstrong west to northwesterly gales over the Bristol Channel(Williams et al. 2012). This depression generated a surge peakof 1.5–2m, which occurred close to the time of high water of alarge spring tide (Heaps 1983; Smith et al. 2012). Little warn-ing was given, and the event resulted in severe flooding anddamage to property and agricultural land from east ofBideford to Gloucester (Uncles 2010). The timing of the pas-sage of the depression, which was coincident with tidal highwater in the Bristol Channel, was a vital contributor to thewater levels produced (Proctor and Flather 1989). This eventwas significant as it highlighted the importance of high-resolution temporal monitoring data during fast moving de-pressions, and reanalysis atmospheric data for the event hasbeen used to test the accuracy of operational forecasting sys-tems (Williams et al. 2012). A larger storm surge (2.4m) in the

Fig. 12 Duration and area ofstorm tide peak exceedingMHWS at Sharpness


Severn Estuary on 24 December 1977 occurred 3 h beforehigh water, giving no cause for concern (Proctor and Flather1989). Surges larger than 2 m rarely occur within 1 h of tidalhigh water in the Severn Estuary due to locally generated tide-surge interaction (Horsburgh and Horritt 2006). However,there is no mechanism to stop the peak of a spring tide andstorm surge coinciding in the Severn Estuary (Pye 2010).

Flood hazard is also increased in the Bay of Fundy whenadverse weather conditions, e.g. a drop in pressure greaterthan 5 kPa, coincides within 1 to 2 h of high water of largespring tides (Greenberg et al. 2012). Significant low-pressure systems have coincided with a very high springtide on only a few occasions; November 1759, October1869, during the Saxby Gale and the 1976 GroundhogDay storm (Desplanque and Mossman 2004). During allevents, seawalls and wharfs were breached, leading to se-vere flooding, damage to boats and infrastructure, and liveslost (Desplanque and Mossman 1999). Storms not occur-ring near high water or on average tides will produce waterlevels within the ‘normal’ range that are often reached byastronomical tides alone (Desplanque and Mossman 1999).The concurrence of the peak of a storm surge with the peakof spring tidal high water could be rare occurrence, butwould cause the greatest impacts on maximum extremewater levels. The timing of surge events is crucial inpredicting extreme water levels and assessing flood hazardin estuaries with a large tidal range (Batstone et al. 2013).

Influence of the Storm Surge Shape

The shape of the storm surge component with time (surgeskewness) influences variability in extreme water levelsand total surge in the Severn Estuary model domain. Asseen in Fig. 6, a storm surge with a positive skewnessappears to create a greater range in maximum water elevationat every point along the deepest channel of the estuary.Positive skewness can act to extend the duration of high water,and therefore increase water volume and surge inflow in theestuary. This could help to amplify the tide further up theestuary (as shallow water effects are reduced) (Proudman1955b). With distance up-estuary, the surge skewness maybecome more negative or more positive consistent with themagnitude of the local interaction growing with tide-surgepropagation up-estuary. The shape and time profile of eachstorm surge generated on the continental shelf varies betweenhistorical extreme water level events, and skewness ofthe storm surge component could be just one of manycharacteristics controlling this driver of flood hazard. Ifshape of a storm surge can be forecast or detected early,then locations in the upper estuary can be warned ofconsequential amplification of the flood hazard.

Previous studies have highlighted the influence surge shapemay have on water levels in the coastal zone (Proudman

1955b; McMillan et al. 2011a). The Environment Agencyhas provided time-integrated duration design surge shapesat tide gauge locations around the UK coastline, from the15 largest ‘skew surge’ events on record (McMillan et al.2011a). The skewness, i.e. the measure of asymmetry, ofthe design surge shapes for tide gauge locations in theSevern Estuary were calculated and shown to have a negativeskewness over a 60-h window (Ilfracombe − 0.46, TheMumbles, − 0.26). These results indicate that storm surgeswith a negative skewness create a constrained range ofextremewater elevations in the Severn Estuary model domain.Therefore, it would be diligent to undertake sensitivity testingof surge skewness derived from historic events to understandvariability in extreme water levels.

Estuarine Form as a Pathway to Increase Flood Hazard

The severity of the extreme water level event, timing andsurge skewness each contribute to the source of a potentialflood event. Pathways are the mechanisms that convey flood-waters from physical drivers, to impact receptors (people,businesses and the built environment). These are often con-sidered to be overland flows, flows in river channels and seadefence overtopping (Narayan et al. 2012). However, it isknown that estuaries and coastal inlets can affect surge andwave propagation in the coastal zone (HRWallingford 2004).Therefore, the geometry, bathymetry and form of the estuaryshould be considered a pathway or source in itself, and influ-ence on flood hazard acknowledge.

The geometry of the Severn Estuary has a strong controlon tide-surge propagation and total surge contribution towater levels. The greatest percentage change in maximumtotal surge elevation in the model domain occurs when thepeak of the surge occurs significantly before or after tidalhigh water, in locations further up-estuary, e.g. Portburyand Sharpness. As the peak of the surge occurs closer tolow water, there may be greater effect bottom friction andshallow water effects on tidal dynamics (Proudman1955b). Flood hazard is reduced when changes in maxi-mum total surge elevation increase. Total surge, includinga meteorological component and tide-surge interactioncomponent, does not appear to contribute to extreme waterlevels, but appears to create variability in extreme waterlevels in the upper estuary.

The smallest change in maximum total surge elevationin the model domain can be seen when the peak of thesurge occurs within 1 h of tidal high water. This is aphenomenon often observed along the west coast ofBritain: if the peak of a storm surge occurs close to thetime of tidal high water then there is very little time forinteractions to develop and little effect of bottom frictiondue to the greater volumetric contribution of the tide andsurge (Proctor and Flather 1989; Horsburgh and Wilson


2007; Jones and Davies 2007). Tide-surge interaction maynot contribute to extreme water levels in the estuary butthe shallow, narrow estuary creates variability whichshould be considered to potentially increase exposure andconsequences of coastal towns in the upper estuary.

The geometry of the estuary has a particularly strongcontrol over the location of maximum tidal range in theestuary, close to Portbury (Figs. 5 and 6). Maximum over-all water elevation in the Severn Estuary model domainconsistently occurs close to Portbury. This is known to beas a result of the funnelling and friction effect in the estu-ary (Dyer 1995). Tides and surges are amplified from thedeeper part of the estuary, through the increasingly narrow,shallow channel towards Portbury (Pye and Blott 2010).This funnelling effect, due to channel convergence, in-creases tidal range to a maximum within the estuary atPortbury (Lennon 1963). The cyclic semi-diurnal tide isanalogous to the incoming resonance from the west sideof the Atlantic Ocean to the east (Gao and Adcock 2016),which further amplifies storm surges up-estuary (Lianget al. 2014). Beyond Portbury, frictional effects controlthe dampening of the tide as energy is lost and the tidalrange decreases (Wolf 1981).

Further to this, human intervention in the estuary itselfcould influence how the physical drivers of flood hazard(‘sources’) move through the estuary. The location and designof sea defences, harbours and interventions (e.g. managedrealignment schemes at Steart Marshes (Wright et al. 2011))would also act to influence the magnitude and variability ofextreme water levels (HRWallingford 2003). These interven-tions would in turn also influence the damage caused andextent of coastal flooding that may be experienced as a resultof the event. River discharge is another pathway to consider,and can induce interactions that lead to increases in the non-tidal residual elevation up to 0.35 m in the Severn Estuary(Maskell et al. 2014).

Flood hazard assessment, and application of the SPRCmodel at a local and regional scale, should consider that theform of a hyper-tidal estuary is a ‘source’ or ‘pathway’ initself, influencing how floodwaters are conveyed through thesystem.

Implications for Local Management Needsin the Severn Estuary and Worldwide

When viewed in an operational context, these results help toidentify contributions to the sources of flood hazard and iden-tify the estuarine form as a source and pathway in itself whichcan act to exacerbate flood hazard. As seen in Fig. 7, theseverity of an event appears to be the most important controlon flood hazard in a hypertidal estuary. The events are stackedas a function of severity, and the 99th percentile event, 3rdJanuary 2014, consistently produces the maximumwater level

through the thalweg. The ‘worst case’ combination of vari-ables to result in greatest flood hazard would be a 99th per-centile event and concurrence of a storm surge peak withpositive skewness and tidal high water. However, it shouldbe considered that accurate bathymetry and boundary forcingdata is important when testing hypothesis in estuaries (Pye andBlott 2014). The accuracy of models which aim to link estu-arine hydrodynamic processes and form, e.g. extreme waterlevels is dependent on accurate bathymetry. The SevernEstuary model is forced at the tidal boundary with data fromone tide gauge, which could limit how accurately water levelsand interactions within the estuary are reproduced. There is aneed for clear, accurate information to inform operationalflood management, with the aim of reducing the hazard fromflood events to the people who are located in flood-proneareas which should utilise the best available data (Pye andBlott 2010).

Freshwater flow can be an important control on tide-surge propagation in some hyper-tidal estuaries (Hoitinkand Jay 2016). River discharge and its associated waterlevels can combine with storm surges driven by the sameweather system (Svensson and Jones 2002), to alter thetiming and magnitude of water levels within the estuary.Nonlinear interactions between extreme river dischargeand storm surges can elevate residual water levels up to0.35 m in idealised estuaries (Maskell et al. 2014), andhave been shown to influence sub-tidal friction and thetiming of high and low water in the River Mahakam,Indonesia (Sassi and Hoitink 2013). Heavy rainfall andspring meltwater, which result in high discharges havebeen shown to inhibit tide-surge propagation up-estuaryin the LaHave Estuary, Nova Scotia (Webster et al.2014); however, dredging activities in the ModaomenEstuary, China, facilitates inland propagation of surgesand can alter salinisation within an estuary (Cai et al.2012). Flood hazard and inundation extents are largelycontrolled by surge elevation, except in the most extremeriver discharge events (Maskell et al. 2014). Freshwaterflow and tide-surge propagation are not statistically inde-pendent (Svensson and Jones 2002), and their combinedimpact is controlled by the timing of peak river discharge,geometry of the estuary and floodplains and human inter-vention within the estuary.

Under changing climate and sea-level rise, the methods andresults presented here could change due to changes in tidalrange, which would alter tide-surge interaction (Robins et al.2016). Deeper water will change frictional influence, and thetipping point between the effect of funnelling and frictioneffect is likely to change. This will have an impact on thelocation of maximum tidal range within the estuary and tidalasymmetry (Robins et al. 2014). In addition to this, rising sealevel may alter channel depths or alter tidal prism (Passeriet al. 2015), therefore fundamentally altering the feedback


between estuarine form and water level. In some coastal re-gions, sea-level rise will increase the magnitude and frequencyof extreme storm events, leading to increased flood hazard(Nicholls et al. 2011; Woodworth et al. 2009). Therefore, theneed for accurate operational forecasting of extreme stormevents will increase under changing climates.

Analysis of barotropic tide-surge propagation in a hyper-tidal estuary has shown sensitivity of coastal flood hazard,generated from the water level boundary conditions, tostorm timing, storm surge shape and event severity. Thisknowledge is of significance to operational modelling forlocal predictions and flood hazard assessments. However,sources of coastal flood hazard are not just limited to thecontributions of astronomical tide and storm surges to waterlevel, but also wave run-up and overwashing or overtopping,driven by coincidental sea state (Prime et al. 2016).Locally-generated wind waves and propagating swellwaves, generated by an offshore storm, which coincidewith an extreme water level can increase flood hazard atthe coast (Wolf 2009; Pye and Blott 2010). Maximumwave height at time of tidal high water can be significantfor coastal flooding (Fairley et al. 2014), and runup asso-ciated with direct wind setup or breaking offshore wavescan influence defence overtopping and breaching (Chenget al. 2015). Future work to consider the influence of swelland wind waves on water levels and uncertainty in waveforcing has the potential to provide improved understand-ing of the combined effect of tide-surge-river-waves onwater levels in a hypertidal estuary. Model outputs from astudy into the combined effect of tide-surge-river-waves onwater levels can be used to force an inundation model(Maskell et al. 2014; Prime et al. 2015), to simulate thearea of maximum inundation from extreme water levelevents. Modelling studies that combine tide-surge-river-wave propagation with depth and extent of inundationcan be effective for floodplain development, flood de-fences and protection for critical infrastructure in theestuary.

Conclusion

There is a need to understand the combination and variabilityof physical drivers contributing to flood hazard in hyper-tidal estuaries, due to their dynamic nature and increasingdevelopment pressures. Delft3D-FLOW is used to simulatetide-surge propagation in a hyper-tidal estuary to under-stand the mechanisms controlling extreme water levels,which contribute to flood hazard. Long-term tide gaugerecords are used to consider the influence of event severity,the timing of the peak of the surge relative to tidal highwater and storm surge skewness on spatial variability ofhistoric extreme water level events in the Severn Estuary

example. Event severity is the most important control onextreme water levels when modelling tide-surge propaga-tion on a local scale. The shape of the storm surge compo-nent with time, classified using surge skewness as a mea-sure of asymmetry, and timing of the storm surge peakrelative to tidal high water influence spatial variability ofwater levels throughout the estuary. Demonstration of theshallow water effect shows the effect estuarine form canhave on the variability of extreme water levels; therefore, itis crucial to have accurate bathymetry and boundary con-ditions to capture these changes throughout the estuary.However, maximum total surge elevation does not appearto significantly contribute to flood hazard as the maximumcontribution occurs during the rise of an adjacent tide tothat of the storm tide. The results can be interpreted in thecontext of the SPRC model, to identify the combined effectof factors which contribute to extreme water levels forlocal scale, flood hazard management. The methodologycan be applied to understand past extreme water levelevents, and in turn help to identify future flood hazard inhypertidal estuaries worldwide.

Acknowledgements The authors thank colleagues at the BritishOceanographic Data Centre (BODC) for providing tidal data; Magnoxfor providing tidal data; Environment Agency for providing tidal data andriver gauge data; Gloucester Harbour Trustees for providing tidal data;and EDINA for bathymetric data. This work was supported by theEngineering and Physical Sciences Research Council as part of theAdaptation and Resilience of Coastal Energy Supply (ARCoES) project,grant number EP/I035390/1.

Open Access This article is distributed under the terms of the CreativeCommons At t r ibut ion 4 .0 In te rna t ional License (h t tp : / /creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you give appro-priate credit to the original author(s) and the source, provide a link to theCreative Commons license, and indicate if changes were made.

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